UK here. Yes, our peanut butter is typically solid and has similar consistency even after a couple months in the larder (never even thought about using the fridge).
Tahini on the other hand separates very quickly into oil+solid so perhaps could also do with a spinner
That’s probably because your peanut butter isn’t just peanuts. If you’re buying Skippy or whatever the additives give it a stable textur. But if you buy pure (aka “natural”) peanut butter you’ll see separation, just like any other nut butter, including tahini
The 100% peanuts varieties separate out a bit due to the oil in the nuts. Most UK supermarkets have an own brand 100% nut option that is usually a good deal compared to the branded stuff like Whole Earth (which has something added/removed to avoid having to stir it I guess).
Same goes for Tahini, you can get bottles that never separate, or jar of 100% sesame seeds that needs a stir.
Tahini on the other hand separates very quickly into oil+solid so perhaps could also do with a spinner